Hochschild cohomology and string topology of global quotient orbifolds

Abstract

Let M be a connected, simply connected, closed and oriented manifold, and G a finite group acting on M by orientation preserving diffeomorphisms. In this paper we show an explicit ring isomorphism between the orbifold string topology of the orbifold [M/G] and the Hochschild cohomology of the dg-ring obtained by performing the smash product between the group G and the singular cochain complex of M.

Revised version. Sections have been reorganized, and section 4.1 is new. Version accepted for publication in the Journal of Topology

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